Minimal Controllability of Conjunctive Boolean Networks is NP-Complete

Abstract Given a conjunctive Boolean network (CBN) with  n state-variables, we consider the problem of finding a minimal set of state-variables to directly affect with an input so that the resulting conjunctive Boolean control network (CBCN) is controllable. We give a necessary and sufficient condition for controllability of a CBCN; an  O ( n 2 ) -time algorithm for testing controllability; and prove that nonetheless the minimal controllability problem for CBNs is NP-hard.

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